1
New Number: 2.52 | AESZ: 16 | Superseeker: 4 644/3 | Hash: 05af0662662bfbec63e3186c4f363313
Degree: 2
\(\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{8} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 168, 5120, 190120, ... --> OEIS Normalized instanton numbers (n0=1): 4, 20, 644/3, 3072, 52512, ... ; Common denominator:...
\((64z-1)(16z-1)\)
| \(0\) | \(\infty\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 64}\) |
|---|---|---|---|
| \(0\) | \(\frac{ 1}{ 2}\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(2\) | \(2\) |
2
New Number: 2.57 | AESZ: 184 | Superseeker: 2 -8 | Hash: ee8bb517b329e58eeb4352dc3cdc3f81
Degree: 2
\(\theta^4-2 x(2\theta+1)^2(11\theta^2+11\theta+5)+2^{2} 5^{3} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 10, 210, 5500, 159250, ... --> OEIS Normalized instanton numbers (n0=1): 2, 4, -8, -194, -2820, ... ; Common denominator:...
\(1-88z+2000z^2\)
| \(0\) | \(\frac{ 11}{ 500}+\frac{ 1}{ 250}I\) | \(\infty\) | \(\frac{ 11}{ 500}-\frac{ 1}{ 250}I\) |
|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(\frac{ 3}{ 2}\) | \(2\) |
3
New Number: 2.60 | AESZ: 18 | Superseeker: 4 364 | Hash: bb479f8a4185bf4a943dba2d433e13e5
Degree: 2
\(\theta^4-2^{2} x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{4} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 108, 3280, 126700, ... --> OEIS Normalized instanton numbers (n0=1): 4, 39, 364, 6800, 662416/5, ... ; Common denominator:...
\(-(16z+1)(64z-1)\)
| \(0\) | \(-\frac{ 1}{ 16}\) | \(\infty\) | \(\frac{ 1}{ 64}\) |
|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(0\) |
| \(0\) | \(1\) | \(\frac{ 3}{ 4}\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 5}{ 4}\) | \(1\) |
| \(0\) | \(2\) | \(\frac{ 3}{ 2}\) | \(2\) |
4
New Number: 3.31 | AESZ: | Superseeker: 4 284 | Hash: 660b0951ad934fc17fda7eb9b1750649
Degree: 3
\(\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{5} x^{2}(2\theta+1)(2\theta+3)(7\theta^2+14\theta+8)-2^{4} 11 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 168, 5360, 210280, ... --> OEIS Normalized instanton numbers (n0=1): 4, 27, 284, 4368, 80968, ... ; Common denominator:...
\(1-80z+896z^2-2816z^3\)
No data for singularities
5
New Number: 3.33 | AESZ: | Superseeker: 4 1580/9 | Hash: da01a7b2dfcebe6e332be6c29ed2a8e5
Degree: 3
\(\theta^4+2^{2} x\left(36\theta^4+72\theta^3+85\theta^2+49\theta+11\right)+2^{4} x^{2}(8\theta^2+16\theta+11)(48\theta^2+96\theta+49)+2^{8} x^{3}(4\theta+7)^2(4\theta+5)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -44, 2244, -122576, 6952516, ... --> OEIS Normalized instanton numbers (n0=1): 4, -25, 1580/9, -1580, 17120, ... ; Common denominator:...
\((16z+1)(1+64z)^2\)
| \(0\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 4}\) |
| \(0\) | \(1\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 4}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 4}\) |
| \(0\) | \(2\) | \(\frac{ 3}{ 2}\) | \(\frac{ 7}{ 4}\) |
6
New Number: 4.37 | AESZ: 206 | Superseeker: 4 284 | Hash: bd5dae321e1369e7fae153775f84a351
Degree: 4
\(\theta^4-2^{2} x\theta(\theta+1)(2\theta+1)^2-2^{5} x^{2}(2\theta+1)(2\theta+3)(11\theta^2+22\theta+12)-2^{4} 3 5^{2} x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)-2^{8} 19 x^{4}(2\theta+1)(2\theta+3)(2\theta+5)(2\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 1200, 44520, ... --> OEIS Normalized instanton numbers (n0=1): 4, 27, 284, 4368, 80968, ... ; Common denominator:...
\(-(16z+1)(4864z^3+896z^2+32z-1)\)
| \(0\) | \(-\frac{ 1}{ 16}\) | \(\infty\) | ≈\(-0.10185-0.013248I\) | ≈\(-0.10185+0.013248I\) | ≈\(0.019489\) | \(s_1\) | \(s_3\) | \(s_2\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(\frac{ 3}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 5}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(\frac{ 7}{ 2}\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) |
7
New Number: 5.108 | AESZ: 365 | Superseeker: 4 1268 | Hash: f84624e83cd4eb2cc90693bd5627efcf
Degree: 5
\(\theta^4-2^{2} x\left(99\theta^4+78\theta^3+65\theta^2+26\theta+4\right)+2^{6} x^{2}\left(938\theta^4+1382\theta^3+1269\theta^2+554\theta+92\right)-2^{10} x^{3}\left(4171\theta^4+8736\theta^3+8690\theta^2+3948\theta+680\right)+2^{15} 5 x^{4}(2\theta+1)(418\theta^3+951\theta^2+846\theta+260)-2^{19} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 720, 44800, 3245200, ... --> OEIS Normalized instanton numbers (n0=1): 4, 107/2, 1268, 89439/4, 396908, ... ; Common denominator:...
\(-(108z-1)(2048z^2-128z+1)(-1+80z)^2\)
| \(0\) | \(\frac{ 1}{ 108}\) | \(\infty\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 2}\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 2}\) | \(\frac{ 1}{ 80}\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(\frac{ 2}{ 3}\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 4}{ 3}\) | \(1\) | \(1\) | \(3\) |
| \(0\) | \(2\) | \(\frac{ 3}{ 2}\) | \(2\) | \(2\) | \(4\) |
8
New Number: 5.112 | AESZ: 395 | Superseeker: 4 940 | Hash: 2d13c01eaf16983977dfb0325c5f376e
Degree: 5
\(\theta^4-2^{2} x\theta(22\theta^3+8\theta^2+5\theta+1)+2^{5} x^{2}\left(34\theta^4-152\theta^3-265\theta^2-163\theta-36\right)+2^{8} x^{3}\left(142\theta^4+600\theta^3+335\theta^2-39\theta-54\right)-2^{11} 3 x^{4}\left(68\theta^4-56\theta^3-295\theta^2-261\theta-72\right)-2^{15} 3^{2} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 1728, 72360, ... --> OEIS Normalized instanton numbers (n0=1): 4, 60, 940, 19091, 463904, ... ; Common denominator:...
\(-(16z+1)(8z+1)(64z-1)(-1+24z)^2\)
| \(0\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 24}\) | \(\infty\) | \(\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 8}\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(\frac{ 5}{ 4}\) | \(2\) | \(2\) |
9
New Number: 10.2 | AESZ: | Superseeker: 4 2252/9 | Hash: 4a65f8c6ad1f8eaf4aa56879ebb94205
Degree: 10
\(\theta^4+2^{2} x\left(69\theta^4+42\theta^3+45\theta^2+24\theta+5\right)+2^{4} x^{2}\left(2097\theta^4+2748\theta^3+3311\theta^2+1990\theta+489\right)+2^{8} x^{3}\left(9240\theta^4+19254\theta^3+26269\theta^2+17979\theta+5020\right)+2^{10} 3 x^{4}\left(34845\theta^4+101230\theta^3+156798\theta^2+120187\theta+36857\right)+2^{12} x^{5}\left(792225\theta^4+2972406\theta^3+5205467\theta^2+4394830\theta+1449907\right)+2^{14} x^{6}\left(4064601\theta^4+18714936\theta^3+36737137\theta^2+33711480\theta+11807867\right)+2^{18} x^{7}\left(3474333\theta^4+18927498\theta^3+41213301\theta^2+40674636\theta+14985820\right)+2^{20} x^{8}\left(7544547\theta^4+47365644\theta^3+113299226\theta^2+119329996\theta+45950951\right)+2^{24} 23 x^{9}(2\theta+3)(50786\theta^3+284985\theta^2+515497\theta+282264)+2^{28} 3 7^{2} 23^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 436, -9872, 228292, ... --> OEIS Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...
\((24z+1)(8z+1)(784z^2+52z+1)(32z+1)^2(736z^2+64z+1)^2\)
| \(0\) | \(-\frac{ 1}{ 23}-\frac{ 3}{ 184}\sqrt{ 2}\) | \(-\frac{ 13}{ 392}+\frac{ 3}{ 392}\sqrt{ 3}I\) | \(\infty\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 23}+\frac{ 3}{ 184}\sqrt{ 2}\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 13}{ 392}-\frac{ 3}{ 392}\sqrt{ 3}I\) | \(-\frac{ 1}{ 8}\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(1\) | \(\frac{ 5}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(4\) | \(2\) | \(3\) | \(1\) | \(4\) | \(2\) | \(2\) | \(2\) |
10
New Number: 10.7 | AESZ: | Superseeker: 4 -628/9 | Hash: d5910f048831bb407eb8998c7c57e09f
Degree: 10
\(\theta^4-2^{2} x\left(48\theta^4+48\theta^3+45\theta^2+21\theta+4\right)+2^{6} x^{2}\left(261\theta^4+489\theta^3+590\theta^2+364\theta+93\right)-2^{6} x^{3}\left(13530\theta^4+35628\theta^3+50795\theta^2+36813\theta+10853\right)+2^{8} 3 x^{4}\left(38616\theta^4+128020\theta^3+206502\theta^2+165712\theta+53013\right)-2^{10} x^{5}\left(685404\theta^4+2714928\theta^3+4854121\theta^2+4193537\theta+1415126\right)+2^{13} x^{6}\left(1419108\theta^4+6542898\theta^3+12841310\theta^2+11823966\theta+4167463\right)-2^{14} x^{7}\left(8117226\theta^4+43045764\theta^3+92299521\theta^2+90336771\theta+33184985\right)+2^{16} x^{8}\left(15319683\theta^4+93106380\theta^3+218052374\theta^2+226725820\theta+86734943\right)-2^{19} 5^{2} x^{9}(2\theta+3)(171838\theta^3+939735\theta^2+1668155\theta+905358)+2^{22} 3 5^{4} 17^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 292, 5728, 115012, ... --> OEIS Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...
\((12z-1)(18496z^3-2352z^2+84z-1)(16z-1)^2(400z^2-32z+1)^2\)
| \(0\) | \(\infty\) | ≈\(0.024764+0.009119I\) | \(\frac{ 1}{ 25}-\frac{ 3}{ 100}I\) | ≈\(0.024764-0.009119I\) | \(\frac{ 1}{ 12}\) | \(\frac{ 1}{ 25}+\frac{ 3}{ 100}I\) | \(\frac{ 1}{ 16}\) | ≈\(0.077634\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(\frac{ 5}{ 2}\) | \(1\) | \(3\) | \(1\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(3\) | \(2\) | \(4\) | \(2\) | \(2\) | \(4\) | \(1\) | \(2\) |
11
New Number: 10.9 | AESZ: | Superseeker: 4 116 | Hash: dbcf215f85612454543d472ffd3bffa9
Degree: 10
\(\theta^4-2^{2} x\left(38\theta^4+70\theta^3+93\theta^2+58\theta+14\right)+2^{4} x^{2}\left(609\theta^4+2214\theta^3+4255\theta^2+4118\theta+1630\right)-2^{8} x^{3}\left(1357\theta^4+7284\theta^3+18055\theta^2+22233\theta+11143\right)+2^{10} x^{4}\left(7450\theta^4+52316\theta^3+157665\theta^2+230387\theta+134924\right)-2^{14} x^{5}\left(6580\theta^4+56446\theta^3+198857\theta^2+332342\theta+219249\right)+2^{16} x^{6}\left(15153\theta^4+151710\theta^3+606095\theta^2+1128594\theta+818733\right)-2^{20} x^{7}\left(5621\theta^4+63496\theta^3+280382\theta^2+568755\theta+444393\right)+2^{22} x^{8}\left(5152\theta^4+63904\theta^3+304853\theta^2+659693\theta+544236\right)-2^{26} 3 x^{9}\left(220\theta^4+2928\theta^3+14781\theta^2+33462\theta+28605\right)+2^{28} 3^{2} x^{10}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 56, 2192, 74112, 2319376, ... --> OEIS Normalized instanton numbers (n0=1): 4, 31/2, 116, 2477/2, 16876, ... ; Common denominator:...
\((1-48z+256z^2)(4z-1)^2(24z-1)^2(8z-1)^2(16z-1)^2\)
| \(0\) | \(\frac{ 1}{ 24}\) | \(\frac{ 1}{ 4}\) | \(\infty\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) | \(0\) | \(1\) | \(0\) | \(1\) |
| \(0\) | \(-2\) | \(3\) | \(\frac{ 7}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(4\) | \(\frac{ 7}{ 2}\) | \(1\) | \(2\) | \(1\) | \(2\) |
12
New Number: 12.4 | AESZ: | Superseeker: 4 -228/5 | Hash: c24070a1d4a449404cd7b46398fa6d6e
Degree: 12
\(5^{2} \theta^4-2^{2} 5^{2} x\left(16\theta^4+32\theta^3+31\theta^2+15\theta+3\right)+2^{4} 5 x^{2}\left(736\theta^4+2368\theta^3+3848\theta^2+2960\theta+915\right)-2^{10} 5 x^{3}\left(304\theta^4+1176\theta^3+2337\theta^2+2313\theta+891\right)+2^{12} 3 x^{4}\left(2608\theta^4+10688\theta^3+21652\theta^2+23580\theta+9945\right)-2^{16} 3 x^{5}\left(2784\theta^4+11616\theta^3+21812\theta^2+22396\theta+9191\right)+2^{21} 3 x^{6}\left(1232\theta^4+5232\theta^3+9332\theta^2+7968\theta+2649\right)-2^{25} 3^{2} x^{7}\left(304\theta^4+1312\theta^3+2472\theta^2+1992\theta+559\right)+2^{30} 3 x^{8}\left(280\theta^4+1216\theta^3+2491\theta^2+2337\theta+827\right)-2^{32} x^{9}\left(1664\theta^4+7200\theta^3+13692\theta^2+11988\theta+3951\right)+2^{38} x^{10}\left(164\theta^4+832\theta^3+1751\theta^2+1731\theta+663\right)-2^{40} x^{11}\left(160\theta^4+928\theta^3+2072\theta^2+2072\theta+777\right)+2^{44} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 108, 688, 3564, ... --> OEIS Normalized instanton numbers (n0=1): 4, -29/5, -228/5, 3724/5, -31856/5, ... ; Common denominator:...
\((16z-1)^2(256z^2-16z+1)^2(4096z^3-768z^2-5)^2\)
| \(0\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 3}I\) | \(\infty\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 3}I\) | ≈\(-0.013312+0.074322I\) | ≈\(0.214124\) | \(\frac{ 1}{ 16}\) | ≈\(-0.013312-0.074322I\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 3}{ 2}\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(3\) |
| \(0\) | \(1\) | \(\frac{ 3}{ 2}\) | \(1\) | \(4\) | \(4\) | \(1\) | \(4\) |
13
New Number: 12.17 | AESZ: | Superseeker: 4 52 | Hash: e65be092d4832d3740d2a3078755f447
Degree: 12
\(\theta^4+2^{2} x\left(24\theta^4+6\theta^3+11\theta^2+8\theta+2\right)+2^{4} x^{2}\left(209\theta^4+2\theta^3+23\theta^2-10\right)+2^{7} x^{3}\left(223\theta^4-1218\theta^3-2225\theta^2-2088\theta-776\right)-2^{10} x^{4}\left(1409\theta^4+9634\theta^3+19337\theta^2+18420\theta+6872\right)-2^{13} x^{5}\left(6527\theta^4+35858\theta^3+78357\theta^2+78428\theta+30414\right)-2^{17} x^{6}\left(6276\theta^4+37704\theta^3+91143\theta^2+97914\theta+40036\right)-2^{21} x^{7}\left(2923\theta^4+22130\theta^3+61939\theta^2+73401\theta+32138\right)-2^{24} x^{8}\left(602\theta^4+10928\theta^3+42765\theta^2+60182\theta+29287\right)+2^{26} x^{9}\left(2352\theta^4+7392\theta^3-7024\theta^2-31968\theta-21891\right)+2^{29} x^{10}\left(1584\theta^4+11904\theta^3+24696\theta^2+19776\theta+4915\right)-2^{35} x^{11}\left(16\theta^4-176\theta^3-784\theta^2-1036\theta-449\right)-2^{39} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 112, -1152, 19216, ... --> OEIS Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...
\(-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(0\) | \(\infty\) | ≈\(-0.057187-0.018391I\) | ≈\(-0.057187+0.018391I\) | \(-\frac{ 1}{ 16}\) | ≈\(0.270624\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 8}\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 3}{ 2}\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(1\) | \(0\) | \(\frac{ 3}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(\frac{ 3}{ 2}\) | \(3\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(\frac{ 3}{ 2}\) | \(4\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) |
14
New Number: 12.5 | AESZ: | Superseeker: 4 2252/9 | Hash: bb257a283455fdd1fa17fef9649505e3
Degree: 12
\(\theta^4+2^{2} x\left(43\theta^4+22\theta^3+25\theta^2+14\theta+3\right)+2^{4} x^{2}\left(753\theta^4+924\theta^3+1107\theta^2+622\theta+141\right)+2^{7} x^{3}\left(3377\theta^4+7218\theta^3+9261\theta^2+5764\theta+1455\right)+2^{10} x^{4}\left(7570\theta^4+24718\theta^3+34375\theta^2+21933\theta+5310\right)+2^{12} 3^{2} x^{5}\left(901\theta^4+5118\theta^3+5777\theta^2-84\theta-1829\right)-2^{14} 3^{2} x^{6}\left(7783\theta^4+33872\theta^3+83851\theta^2+107556\theta+49489\right)-2^{17} 3^{3} x^{7}\left(4895\theta^4+28154\theta^3+69267\theta^2+83564\theta+36929\right)-2^{20} 3^{4} x^{8}\left(44\theta^4+528\theta^3+247\theta^2+240\theta+274\right)+2^{23} 3^{5} x^{9}\left(664\theta^4+4760\theta^3+13781\theta^2+17353\theta+7679\right)+2^{26} 3^{6} x^{10}(\theta+1)(109\theta^3+651\theta^2+1373\theta+933)-2^{29} 3^{7} x^{11}(\theta+1)(\theta+2)(27\theta^2+153\theta+199)-2^{33} 3^{9} x^{12}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -12, 180, -2736, 42948, ... --> OEIS Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...
\(-(16z+1)(432z^2+36z+1)(24z+1)^2(288z^2+48z+1)^2(8z-1)^3\)
| \(0\) | \(-\frac{ 1}{ 12}+\frac{ 1}{ 24}\sqrt{ 2}\) | \(-\frac{ 1}{ 12}-\frac{ 1}{ 24}\sqrt{ 2}\) | \(-\frac{ 1}{ 24}\) | \(\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\infty\) | \(-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(2\) | \(1\) |
| \(0\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(\frac{ 3}{ 2}\) | \(1\) | \(1\) | \(2\) | \(1\) |
| \(0\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(2\) | \(3\) | \(2\) |
15
New Number: 13.10 | AESZ: | Superseeker: 4 -628/9 | Hash: 2a9fda379889eb2fd218bd01f2520f7a
Degree: 13
\(\theta^4-2^{2} x\left(35\theta^4+38\theta^3+35\theta^2+16\theta+3\right)+2^{4} x^{2}\left(546\theta^4+1068\theta^3+1287\theta^2+790\theta+201\right)-2^{6} x^{3}\left(4928\theta^4+12888\theta^3+17829\theta^2+12673\theta+3693\right)+2^{8} x^{4}\left(28123\theta^4+88408\theta^3+131977\theta^2+98226\theta+29511\right)-2^{10} 3^{2} x^{5}\left(11315\theta^4+41094\theta^3+65088\theta^2+47691\theta+13532\right)+2^{13} 3^{2} x^{6}\left(11674\theta^4+48674\theta^3+79399\theta^2+52683\theta+11716\right)-2^{15} 3^{3} x^{7}\left(2063\theta^4+11102\theta^3+11184\theta^2-9217\theta-10762\right)-2^{17} 3^{4} x^{8}\left(3277\theta^4+16284\theta^3+42329\theta^2+57018\theta+27266\right)+2^{20} 3^{5} x^{9}\left(1124\theta^4+7114\theta^3+18121\theta^2+22265\theta+10018\right)+2^{24} 3^{6} x^{10}(\theta+1)(\theta^3-105\theta^2-277\theta-267)-2^{25} 3^{7} x^{11}(\theta+1)(\theta+2)(93\theta^2+441\theta+607)+2^{27} 3^{10} x^{12}(\theta+3)(\theta+2)(\theta+1)(\theta+6)+2^{30} 3^{10} x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 180, 2928, 47556, ... --> OEIS Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...
\((8z-1)(10368z^3-1728z^2+72z-1)(12z-1)^2(288z^2-24z+1)^2(4z+1)^3\)
| \(0\) | \(\infty\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 24}I\) | ≈\(0.112601\) | \(\frac{ 1}{ 8}\) | ≈\(0.027033+0.011216I\) | \(-\frac{ 1}{ 4}\) | \(\frac{ 1}{ 12}\) | ≈\(0.027033-0.011216I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 24}I\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(2\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(3\) | \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) |
| \(0\) | \(4\) | \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(1\) | \(2\) | \(4\) |
16
New Number: 13.3 | AESZ: | Superseeker: 4 52 | Hash: 9127ce057848ca38f220a7bb67e245a2
Degree: 13
\(\theta^4-2^{2} x\left(38\theta^4+50\theta^3+53\theta^2+28\theta+6\right)+2^{4} x^{2}\left(617\theta^4+1598\theta^3+2361\theta^2+1812\theta+586\right)-2^{8} x^{3}\left(1422\theta^4+5468\theta^3+10321\theta^2+9918\theta+3961\right)+2^{11} x^{4}\left(4165\theta^4+21060\theta^3+48228\theta^2+54855\theta+25440\right)-2^{14} x^{5}\left(8248\theta^4+50660\theta^3+135119\theta^2+175776\theta+91644\right)+2^{16} x^{6}\left(23161\theta^4+161282\theta^3+479205\theta^2+690060\theta+393943\right)-2^{20} x^{7}\left(12116\theta^4+89614\theta^3+279997\theta^2+425868\theta+256804\right)+2^{23} x^{8}\left(9924\theta^4+74644\theta^3+231233\theta^2+346097\theta+206261\right)-2^{27} x^{9}\left(3250\theta^4+24820\theta^3+75837\theta^2+107033\theta+58293\right)+2^{28} x^{10}\left(6672\theta^4+52000\theta^3+164304\theta^2+235440\theta+126113\right)-2^{32} x^{11}\left(1312\theta^4+10208\theta^3+32688\theta^2+49072\theta+28407\right)+2^{36} x^{12}\left(192\theta^4+1568\theta^3+4952\theta^2+7144\theta+3959\right)-2^{40} x^{13}\left((2\theta+5)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 464, 8832, 178960, ... --> OEIS Normalized instanton numbers (n0=1): 4, 7/2, 52, 500, 2796, ... ; Common denominator:...
\(-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3\)
| \(0\) | ≈\(0.005863+0.196043I\) | \(\infty\) | ≈\(0.005863-0.196043I\) | ≈\(0.050774\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(\frac{ 5}{ 2}\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(\frac{ 5}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(0\) | \(1\) |
| \(0\) | \(3\) | \(\frac{ 5}{ 2}\) | \(3\) | \(3\) | \(-1\) | \(1\) | \(0\) | \(1\) |
| \(0\) | \(4\) | \(\frac{ 5}{ 2}\) | \(4\) | \(4\) | \(1\) | \(2\) | \(0\) | \(2\) |
17
New Number: 6.30 | AESZ: | Superseeker: 4 436 | Hash: bc45bbf252bff0ad05b31f8e076f64cb
Degree: 6
\(\theta^4+2^{2} x(\theta^2+\theta+1)(18\theta^2+18\theta+5)+2^{4} x^{2}\left(39\theta^4+156\theta^3+337\theta^2+362\theta+135\right)-2^{6} x^{3}\left(1124\theta^4+6744\theta^3+14434\theta^2+12954\theta+4329\right)-2^{8} 3 7 x^{4}\left(445\theta^4+3560\theta^3+10034\theta^2+11656\theta+4779\right)-2^{10} 3^{2} 7^{2} x^{5}(\theta+4)(\theta+1)(62\theta^2+310\theta+345)-2^{12} 3^{4} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 480, -11264, 285712, ... --> OEIS Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...
\(-(-1+36z)(12z+1)^2(28z+1)^3\)
| \(0\) | \(-\frac{ 1}{ 28}\) | \(\infty\) | \(-\frac{ 1}{ 12}\) | \(\frac{ 1}{ 36}\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(1\) | \(0\) | \(0\) |
| \(0\) | \(0\) | \(2\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(-\frac{ 1}{ 4}\) | \(4\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(\frac{ 1}{ 4}\) | \(5\) | \(1\) | \(2\) |
18
New Number: 8.66 | AESZ: | Superseeker: 4 12332 | Hash: d941d8e5d41f2e7285be47b4fbc81023
Degree: 8
\(\theta^4-2^{2} x\left(12\theta^4-24\theta^3-23\theta^2-11\theta-2\right)-2^{7} x^{2}\left(32\theta^4+392\theta^3+484\theta^2+223\theta+41\right)+2^{12} x^{3}\left(31\theta^4-30\theta^3-872\theta^2-801\theta-217\right)-2^{16} 3 x^{4}\left(140\theta^4+60\theta^3-1332\theta^2-971\theta-231\right)-2^{20} x^{5}\left(772\theta^4+7960\theta^3+7483\theta^2+1509\theta-266\right)+2^{26} x^{6}\left(46\theta^4+2766\theta^3+2333\theta^2+672\theta+19\right)-2^{30} 5 x^{7}\left(477\theta^4+930\theta^3+697\theta^2+232\theta+28\right)-2^{36} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 424, -6272, 859816, ... --> OEIS Normalized instanton numbers (n0=1): 4, 500, 12332, 358180, 15491360, ... ; Common denominator:...
\(-(64z+1)(4096z^3+6144z^2+48z-1)(1-32z+2560z^2)^2\)
| \(0\) | \(-\frac{ 1}{ 64}\) | \(\infty\) | \(\frac{ 1}{ 160}-\frac{ 3}{ 160}I\) | ≈\(-1.492036\) | ≈\(0.009415\) | ≈\(-0.017379\) | \(\frac{ 1}{ 160}+\frac{ 3}{ 160}I\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(0\) | \(2\) | \(1\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) |
19
New Number: 8.69 | AESZ: | Superseeker: 4 52 | Hash: e303d10e77a367612be2fb706f37b895
Degree: 8
\(\theta^4-2^{2} x\left(20\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(125\theta^4+362\theta^3+471\theta^2+284\theta+66\right)-2^{7} x^{3}\left(191\theta^4+606\theta^3+855\theta^2+588\theta+154\right)+2^{10} x^{4}\left(192\theta^4+552\theta^3+562\theta^2+268\theta+49\right)-2^{13} x^{5}\left(134\theta^4+380\theta^3+373\theta^2+124\theta+3\right)+2^{16} x^{6}\left(61\theta^4+150\theta^3+173\theta^2+93\theta+19\right)-2^{19} x^{7}\left(19\theta^4+50\theta^3+56\theta^2+31\theta+7\right)+2^{23} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 128, 2816, 74896, ... --> OEIS Normalized instanton numbers (n0=1): 4, 15/2, 52, 1563/2, 7276, ... ; Common denominator:...
\((16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2\)
| \(0\) | \(\infty\) | \(\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 7}I\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 7}I\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(3\) |
| \(0\) | \(1\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(4\) |
20
New Number: 8.74 | AESZ: | Superseeker: 4 436 | Hash: a0fbd8561e58a032d489a1dabee1e026
Degree: 8
\(\theta^4-2^{2} x\theta(22\theta^3+14\theta^2+9\theta+2)+2^{4} x^{2}\left(109\theta^4-74\theta^3-293\theta^2-258\theta-80\right)+2^{8} x^{3}\left(39\theta^4+414\theta^3+674\theta^2+504\theta+144\right)-2^{10} x^{4}\left(405\theta^4+1170\theta^3+1321\theta^2+424\theta-104\right)-2^{14} x^{5}(\theta+1)(12\theta^3+558\theta^2+1495\theta+1255)+2^{16} x^{6}(\theta+1)(\theta+2)(467\theta^2+1593\theta+1540)-2^{20} 5 x^{7}(\theta+3)(\theta+2)(\theta+1)(\theta-40)-2^{22} 5^{2} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 80, 1536, 56592, ... --> OEIS Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...
\(-(-1+56z)(20z-1)^2(8z-1)^2(8z+1)^3\)
| \(0\) | \(\frac{ 1}{ 56}\) | \(\infty\) | \(\frac{ 1}{ 20}\) | \(-\frac{ 1}{ 8}\) | \(\frac{ 1}{ 8}\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(1\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(2\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(3\) | \(3\) | \(-\frac{ 1}{ 4}\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(2\) | \(4\) | \(4\) | \(\frac{ 1}{ 4}\) | \(1\) |